Question: Consider the vector space of real-valued functions with basis (sin(x), cos(x)). Show that (2 sin(x) + cos(x), 3 cos(x)) is also a basis for this

Consider the vector space of real-valued functions with basis (sin(x), cos(x)).
Show that (2 sin(x) + cos(x), 3 cos(x)) is also a basis for this space. Find the change of basis matrix in each direction.

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